| An Investigation on Left Hyperideals of Ordered Semihypergroups |
| Received:January 20, 2016 Revised:May 24, 2017 |
| Key Words:
ordered semihypergroup minimal left hyperideal maximal left hyperideal weakly prime left hyperideal quasi-prime left hyperideal weakly quasi-prime left hyperideal
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11361027), the University Natural Science Project of Anhui Province (Grant No.KJ2015A161), the Natural Science Foundation of Guangdong Province (Grant No.2014A030313625) and the Key Project of Department of Education of Guangdong Province (Grant No.2014KZDXM055). |
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| Abstract: |
| In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore, we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasi-prime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover, we give some characterizations of weakly quasi-prime left hyperideals by the left hyperideals and weakly $m$-systems. We also characterize the quasi-prime left hyperideals in terms of the $m$-systems. In particular, we prove that an ordered semihypergroup $S$ is strongly semisimple if and only if every left hyperideal of $S$ is the intersection of all quasi-prime left hyperideals of $S$ containing it. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2017.04.004 |
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